Atomic scattering factors for spherical and aspherical charge distributions

The atomic scatteritng factors for forty-five atoms and ions were calculated from Hartree and Hartree Fock SCF wave functions and compared with the results of James & Brindley, Berghuls et al., and others. Principal scattering factors were also calculated along the lines of McWeeny for a number of atoms containing aspherical charge distributions of p electrons. A general formalism for calculating the coherent scattering of x-rays from nonspherical charge distributions as a function of atomic orientation is presented, based in part on group theoretic methods. For p electrons the results of McWeeny are reproduced. For d electrons, the scattering is completely described in terms of three principal scattering factors and the angle between the scattering vector and the atomic orientation. As illustration, specific numerical calculations are given for several atoms with incomplete d shells. A discussion of the relationship between this treatment and the usual spherical approximation is presented. (auth)